What follows is a list of some of the behaviours one will expect to observe in mathematically gifted students in their classroom. It is important to note that this list is not exhaustive, nor is it prescriptive. It should not be used as a basis to label students, nor is it expected that gifted students will show all of these behaviours. These behaviours are most likely to be seen in a learning environment suitable for gifted students. These are adapted from Gifted and Talented Students (Moltzen, Riley & McAlpine, 2000)
Learning characteristics
Displays logical and analytical thinking
Is quick to see patterns and relationships
Masters new content quickly
Stives for accuracy in solutions
Easily grasps underlying principles
Likes intellectual challenge
Jumps stages in learning, or in problem solving
Seeks to redefine problems
Finds as well as solves problems
Reasons things out for him- or her-self
Formulates and supports ideas with evidence
Can recall a wide range of knowledge
Independently seeks to discover the why and how of things
Creative thinking characteristics
Produces original ideas
Displays intellectual playfulness
Demonstrates awareness of aesthetic qualities in mathematical expressions
Generates a large number of ideas
Takes academic risks
Experiments with new and novel ways of solving problems
Seeks to discover unconventional relationships
Motivational characteristics
Strives for high standards of personal achievement
Is self-directed
Is highly self-motivated and sets personal goals
Is persistent in seeing problems to completion
Becomes absorbed in problems
Tends to be self-critical and evaluative
May prefer to work independently
These characteristics closely relate to the three concepts in Renzuli's 'Three-ring' model. It is important to note that many students may display many characteristics from one set, and few from another. In particular a large number of gifted students find school un-motivating and therefore show few characteristics from the last set. Another factor to be aware of is that many of these characteristics may be displayed in the classroom in negative rather than positive ways. this could include:
A knowledgeable student dominates the classroom discussion
A student who learns rapidly, may complete work and then appear to be off-task
A student who strives for accuracy may constantly correct other students, and the teacher
A student with intellectual playfulness may not be paying attention in class
A student may become absorbed in a problem that is not related to schoolwork
A student may resist working in groups as they profer to work independently
A perfectionist student may avoid some tasks for fear of failure
There are many ways a student may display 'bad' behaviour if they are bored and frustrated with an unsuitable programme
Characteristics of gifted mathematics students
What follows is a list of some of the behaviours one will expect to observe in mathematically gifted students in their classroom. It is important to note that this list is not exhaustive, nor is it prescriptive. It should not be used as a basis to label students, nor is it expected that gifted students will show all of these behaviours. These behaviours are most likely to be seen in a learning environment suitable for gifted students. These are adapted from Gifted and Talented Students (Moltzen, Riley & McAlpine, 2000)
Learning characteristics
Creative thinking characteristics
Motivational characteristics
These characteristics closely relate to the three concepts in Renzuli's 'Three-ring' model. It is important to note that many students may display many characteristics from one set, and few from another. In particular a large number of gifted students find school un-motivating and therefore show few characteristics from the last set. Another factor to be aware of is that many of these characteristics may be displayed in the classroom in negative rather than positive ways. this could include: